Rigid Object In Static Equilibrium

I am currently reading the about the topic mentioned in the title of this thread. In my textbook, the author gives the example with the wine-bottle and it's holder (I attached a photo). In this example, the author states that in order for this to be in static equilibrium, the second condition, [itex]\sum \vec{\tau}_{ext}=0[/itex], which can only be satisfied when the center of gravity of the system is directly over the support point.

Could someone explain why the center of gravity has to be directly over the support?

Ask yourself what would happen if the 'center of gravity' (the effective point at which the force of gravity acts on a rigid body) were to be outside of the support zone. Would there be a net torque? If so, how much and in what direction?